{
  "id": "0903.1117",
  "version": "v3",
  "published": "2009-03-05T22:33:49.000Z",
  "updated": "2009-03-11T17:26:19.000Z",
  "title": "Control theory and the Riemann hypothesis: A roadmap",
  "authors": [
    "Markku Nihtilä"
  ],
  "comment": "7 pages, some references corrected",
  "categories": [
    "math.NT"
  ],
  "abstract": "An alternative way of looking at the Riemann hypothesis from the viewpoint of mathematical control theory is considered. A control theoretic transfer function is constructed by inverting the values of the Riemann zeta-function from which the unstable pole at s=1 has been stripped off. A series expansion is developed for the impulse response of the control system via inverse Laplace transformation. If the series converges and the unproved growth conjecture of the impulse response is true, then the Riemann hypothesis is also true.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-03-11T17:26:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "93D99"
    ],
    "keywords": [
      "riemann hypothesis",
      "control theoretic transfer function",
      "impulse response",
      "inverse laplace transformation",
      "unproved growth conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1117N"
    }
  }
}